While Russian motorized convoys headed toward the capital Kiev, the United Nations said more than 500,000 Ukrainian refugees had fled to neighboring countries since February 24.
At the Budapest train station, Mr. Amir, who had just evacuated to Hungary, expressed concern for his sons remaining in Kiev and wondered if one day he would be able to return home.
`I think fighting will continue for a long time,` he said.
Ukrainian refugees arrive at Medyka border gate in Poland on February 28.
At the Hungarian border, near the village of Tiszabecs, a young mother traveling with her son recounted how scared and nervous they were when they saw rockets flying overhead while driving for four days from Kiev to here.
`I saw the fighting, I saw the rockets,` Ivan, 15, said.
The flow of new people continues to flow to border crossings in Central Europe in the context of war tensions in Ukraine that show no signs of cooling down.
Across Central Europe, officials set up tent reception centers where people can receive medical aid and process asylum documents.
Most evacuees arrived in the EU from border areas in eastern Poland, Slovakia and Hungary as well as in northern and northeastern Romania.
Poland, with a Ukrainian population of about one million people, the largest in the region, has welcomed large numbers of refugees.
At the Medyka border crossing, Poland’s busiest along the roughly 500km border with Ukraine, people sat huddled around fires in freezing temperatures as they waited for buses to take them to reception centers.
Refugees from Ukraine to Poland light a fire to warm themselves at the Rava Ruska border checkpoint, in the west of the country, on February 26.
Some refugees were picked up by family members who had previously worked in the EU.
Hungarian police report more than 60,000 people have entered the country since Russia launched its military campaign, while nearly 90,000 have entered Romania.
At some border gates, the line of people lining up on the Ukrainian side is several kilometers long.
Ibrahima Sory Keita, who came from the West African country of Guinea to study abroad in the Ukrainian city of Meliptopol three weeks ago, arrived at the Medyka border gate to enter Poland.
Besieged cities across Ukraine are home to tens of thousands of African students studying medicine, engineering and the military.
Keita and several friends ran to the border when fighting broke out and had to walk the last 45 km.